I recently posted a photograph on an Australian forum and someone commented they thought I would get more detail as I'd used f22. Someone else commented that the Nikon f22 was equivalent to the Canon f11 - is this true?

As a general rule, lenses will have a performance peak. i.e. contrast, saturation and sharpness may not be at the highest level wide open (e.g. f3.5), but stopping down 1 or 2 stops yields the best image quality. You'll then have peak quality for a few stops, but an increasing depth of field before diffraction starts to take effect, which results in a drop off on performance.

There are exceptions to the rule (Macro lenses at high f numbers can have less drop off in image quality, high quality pro zooms and prime lenses can be at their best wide open) but you pay for it.

The shot in the post was a macro shot with a macro lens - I've just posted it in the macro section on this forum - it's the one of the spider with the hoverfly and I was really pleased with the detail.

I can't think of an applicable scenario where N f/22 = C f/11 would apply here. Just doesn't make sense.

And dubaiphil's "Diffraction can start to occur earlier on full frame camera bodies." there's two effects I'd say make the opposite the case. One is that pixels are generally smaller on crop sensors so pixel level diffraction softening would occur first on a crop sensor as you stop down compared to full frame. Also ignoring the pixels in bigger picture view, you would still need to stop down further on a full frame for equivalence to crop sensor.

I'd like to comment on the "diffraction can start to occur earlier on full frame camera bodies.", too, Dubaiphil:
If you're not into pixel-peeping where (almost) everything depends on the size of the individual pixels it generally holds true that diffraction starts 1 stop later on FF/FX-bodies than on DX/APS-C bodies.
But as Canon APS-C and Nikon DX bodies have almost the same sensor size you can bet any amount of money that the N-f/22 = C-f/11 is utter B.S.

From my current testing of the two DX macro-lenses from Nikon I can attest to f/8 being the sharpest and diffraction visibly setting in at f/11 (but only if you look very close). At f/16 it is more easily visible and at f/22 (and beyond) it really gets bad.
With macro shots you always have to balance the gain in dof and the loss of overall sharpness when stopping down. So in this case a shot at f/16 might even produce a more satisfying photo than f/8.

An f-stop is an f-stop, but I can see why the confusion might arise. Unit-focusing lenses get slower, i.e. have a higher minimum f-stop, when focused closer. Nikon macro lenses report this change, but Canon lenses don't. So if you're shooting at life-size magnification with an f/2.8 Canon macro at full aperture, it will report f/2.8. A Nikon f/2.8 macro in the same situation will report f/5.6. Stopping down the Canon to f/11 would in this case provide a true f/22, equal to the Nikon at its reported f/22.

Modern macro lenses aren't unit-focusing, but the general principles above still apply (to differing degrees, depending on the lenses in question).